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Dec182010

Solitary Physics

In many different physical systems, complex (i.e. non-linear) and delicately balanced interactions between microscopic constituents can collude to form configurations known as solitons. This phenomenon arises in systems as disparate as fluid dynamics, superconductivity, and string theory. In all cases, solitons share common attributes and play a central role in understanding the physical system as a whole. In addition, solitons are some of the most beautiful mathematical constructs that arise in physics.

Imagine a long chain of pendulae, connected to each other by flexible springs. You may want to watch the first video attached to this post at this point to visualize the setup. If you perturb a pendulum in the chain by a small amount - say by bumping it slightly - you'll generate a small disturbance that travels along the chain. A much more interesting thing happens if you grab one of the pendulae and rotate it a full circle: this creates a twist in the chain. When you let go, the localized twist in the chain propagates along it much like a particle would (see first video). This is a soliton: a configuration arising from the strong interactions between the constituents of a system (i.e. the pendulae) - hence forming a collective entity (i.e. the twist) that propagates and behaves coherently much like a solitary particle. All solitons carry energy (or mass) inversely proportional to the strength of the interactions in the system: the stronger the interactions, the lighter or less energy the soliton would have. All solitons preserve their shape and a finite size (which is again inversely proportional to the strength of the interactions) as they propagate. In realistic scenarios like the one depicted in the videos, frictional effects eventually dissipate and unravel the soliton. But notice how long the pendulum twist lives before dissipating! All solitons have a "topological" mechanism that assure their stability. In the case of the pendulae chain, this topological element is the twist in the chain: to disentangle the soliton, you would need to untwist the entire chain which requires a rather large effort - hence the robustness and stability of the pendulum soliton. 

The second video shows a soliton propagating on the surface of water. In this case, you also can see the interactions of two solitons! The two water wave solitons repel each other, yet preserve their shapes after the collision - much like particles! Tsunamis in the ocean can be solitonic and pack a devastating blow when they hit a shoreline. The last video shows toroidal bubble solitons created by dolphins and whales, and even a smoke toroid generated by a nuclear explosion… Other examples of solitons include vortices in superconductivity (see previous post on type II superconductors), vortices in superfluids, and even D-branes in string theory (more on this later)…

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